I'd be interested to hear anything on this too, as I'm playing a game at the moment in which the three custom races are being whupped by me and the more standard races.
I've observed (I'm not sure how accurately) that some AIs seem to be more robust than others: Terrans, Krynn and Thalans (bloody Super Hiver no doubt helping the latter) usually give me the best run for my money and play a reasonably balanced game. Drengin and Yor do their thing very well at the start but I always beat them down in the end due to their refusal to develop engine techs and my ability to build alliances against them. Likewise Arceans, although I've seen them shine on occasion. Altarians have always been largely pacifist (as you might expect), except for the time I gifted them lots of high-tech weapons, at which point they went on an invasion spree, which was a big surprise (we were allied and they kept dragging me into their wars). The Iconian AI doesn't seem to do anything much, whereas converesly the Korath scares the bejeebus out of me, but I don't have much experience with either at higher levels and I don't know much about how either strategy works without bonuses/abilities. I switched the Iconians to have the Krynn AI in my current game and they've been quite formidable even with a second-rate ability and not-as-good bonuses as the Kyrnn themselves. The Korx just seem to trade as far as I can tell and don't seem to progress too well into the later game, although they've been better ship builders than some others so can give me a decent fight sometimes. Generic doesn't seem up to much at all, judging by the performance of my custom races who have used it to date.
The one AI that drives me nuts though is the Torian. They suck up to me even if I'm blatantly evil, but if I ally with them they get into every possible war and demand I rescue them. The AI seems to struggle with building any kind of remotely useful warship, so in recent games I've derived no small pleasure from making Torians into my whipping boys - something which they whine about no end.
Are these random observations any use? Sorry I can't be more help, still not that experienced a player myself.